I present a new low discrepancy quasirandom sequence that offers substantial improvement over current state-of-the art sequences eg Sobol, Niederreiter,…

# The Unreasonable Effectiveness

# Evenly distributing points on a sphere

How to distribute points on the surface of a sphere as evenly as possibly is an incredibly important problem in maths, science and computing, and mapping the Fibonacci lattice onto the surface of a sphere via equal-area projection is an extremely fast and effective approximate method to achieve this. I show that with only minor modifications it can be made even better.

# What is the 3rd most irrational number?

The answer will surprise you!Most of us know about the golden ratio, \(\phi = \frac{1+\sqrt{5}}{2} \) and how it can be considered the most irrational number, but most people never ask the question, “What is the second and third most irrational number?” In this post, I discuss discuss some special irrational numbers, and why they can be considered the 2nd and 3rd most irrational numbers. Finding good rational approximations to reals. In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The problem on how well a real number can be approximated by rational numbers is…

# Efficient methods to estimate accuracy and variance

for quasi-monte carlo integration.In this brief post, I describes various methods to estimate uncertainty levels associated with numerical approximations of integrals based on quasirandom Monte Carlo (QMC) methods.

# Using quasirandom sequences to evenly sample discrete distributions.

I show how to construct anĀ infinite sequence of samples from a set $S$, such that for all $m>0$, the first $m$ terms of the sequence, all subsets of $S$ occur as evenly as possible.